Section 1

What do you see?

There's a boy sitting in a wheely chair and he's being pushed by a girl. In a thought bubble you see a roller coaster but she's actually just moving him and he is blindfolded so he thinks that he is on a ride. She changes direction and speed to confuse him.

What do you think?

The drop after the hills and the loops produce the most fear because they're unexpected and dangerous.

Look up roller coaster design on the Internet and list at least two roller coasters mentioned, Describe their most important features.

Kingda Ka

Six Flags, Jackson, NJ

The fierce Kingda Ka is the tallest coaster in the World, fastest in North America.This remarkable thrill ride breaks all world records for coaster speed and height, zooming from 0 to 128 mph in 3.5 seconds and catapulting you 45 stories into the sky.

www.sixflags.com



El Toro
Six Flags, Jackson, NJ

Inspired by the strength and bravery of a bull-taming matador, El Toro features the steepest drop of any wooden roller coaster in the country at a record-breaking 76 degrees. This imposing thrill ride combines all the best features of wooden coasters with the smooth speed of their steel counterparts.

www.sixflags.com



Physics Talk

• scalar- a measurement that has magnitude but not direction
• speed- the distance traveled divided by the time
• vector- a measurement that includes magnitude and direction
• displacement- the change in position
• velocity- displacement divided by the time
• acceleration- the change in velocity divided by the time

Checking Up

1.

• it has no direction and the displacement is direction, so the displacement would be 0.

2.

• The displacement would be 0 for anything where you go there and back because you are starting and ending in the same place. .

3.

• The speed is distance divided by time and then the velocity is displacement divided by time

4.

• The acceleration is the change in velocity divided by the time

Physics to Go

1.
2.

• They will scream the most on the curves the drops and the loops.

3.

• La Paz is the fastest
• v = displacement divided by time
• 40000 km / 24 h
• 1666.7 km/h
• no acceleration

4.

• a = delta v / delta t
• a = 16 m/s - 4 m/s / 3s
• a = 4 m/s/s

5.

• car traveling at 50 km/h - speed
• student riding bike at 5 m/s toward home - velocity
• roller coaster whips around a left turn at 5 m/s - velocity, acceleration
• roller coaster dragged up a hill 12 m tall traveling at 3 m/s - displacement, velocity
• train ride takes you 150 km - displacement

6.

• v = displacement divided by time
• v = .1m / 2s
• .05 m/s
• 7. v = displacement / time
• .05 m/s = .05 m/s
• 1

8.

• a = change in V / change in t
• a = 25 m/s / 10s
• a = 2.5 m/s^2

10.

• If I had to add 2 more changes to it for children I would make the hills smaller i would take out the loops and i would make the turns wider.

Section 2

What do you see?

A cart following a path, the people in the car look bored and then in the other cart the people are screaming because they're going down a hill and the other people are just going in a straight line.

What do you think?

The larger the angle the better the ride will be.

Physics Talk

• GPE and KE
• Energy Change
• GPE- the energy a body possesses as a result of its position on a gravitational field
• KE- the energy an object has because of its speed
• KE- speed
• GPE- height
• GPE and KE- mass
• GPE = mgh
• KE = 1/2mv^2
• KE plus EPE - mechanical energy
• KE plus GPE - always remains the same
• GPE ^ KE goes down
• all mechanical energy is equal
• the bottom will always be equal to the top
• KE bottom = GPE top

Checking Up

1.

• The larger the angle the larger the acceleration

2.

• When the high changes the GPE does also, same with the mass too, if it increases GPE will increase

3.

• When the speed of an object increases the KE and the mass increase.

4.

• The GPE will decrease because the height is getting smaller but the KE will increase.

5.

• It has 30,000 J KE 3/4 the way down

Physics to Go

1.

• They're the same when they get to the bottom

3.

height (m)	GPE =mgh	KE = 1/2mv^2	GPE + KE
top (30)	60,000	0	60,000
bottom (0)	0	60,000	60,000
halfway down (15)	30,000	30,000	60,000
3/4 way down (7.5)	15,000	45,000	60,000

4
8.

• The mass doesn't matter so the speed won't change.

9.

• The fastest speed is at point B because the height was the highest.
• The same speed at points C and F because the height is the same.
• It's traveling faster at D because it just dropped.

5.

height (m)	GPE (J) = mgh	KE (J)= 1/2mv^2	GPE + KE (J)
top (25 m)	75,000	0	75,000
bottom (0 m)	0	75,000	75,000
halfway down (12.5 m)	37,500	37,500	75,000
further down (5 m)	15,000	60,000	75,000

6.

• GPE = mgh
• (300)(10)(25)
• 75,000
• then replace h with 0, 12.5, and 5

7.

• GPE = mgh
• (.2)(9.8)(.75)
• 1.47 J
• GPE = KE
• mgh = 1/2mv^2
• (9.8)(.75) = 1/2v^2
• 3.83 m/s = v
• GPE = KE
• mgh = 1/2mv^2
• (9.8)h = 1/2(3.83)^2
• h = .75 m

10.

• I would be impossible to get to H because the GPE has an original hight that is much smaller than the height of H. H would turn out being so much higher than the GPE so that as a result they won't end up being equal in the end.

11.

Position	Height (m)	GPE = mgh (J)	KE = 1/2mv^2 (J)	GPE + KE (J)
bottom of hill	0	0	50,000	50,000
top of hill	25	50,000	0	50,000
top of loop	15	30,000	20,000	50,000
horizontal loop	0	0	50,000	50,000

What do you think now?

• The speeds at the bottom of the roller coaster for each will both have the same speed because they are both left off from the same initial height, but i think that the roller coaster that's on the right will be much more fun because there is a bigger drop in where the acceleration will probably be much bigger. If i had to do on a roller coaster i would definitely choose that one even though it does look more dangerous!

Section 3

What do you see?

• The kids are trying to fine the GPE of a spring toy and they and trying to also find the speed. You can see one kid holding a meter stick to see how high the toy goes, which is a necessary variable in trying to find the GPE. It also appears as if the kids are using a photo-gate timer to determine the exact speed.

What do you think?

• By using electricity energy and the cables that pull a roller coaster it can reach its highest point. It wouldn't cost more to ride a roller coaster full of people rather than an empty one because the end result will always be the same as an end result.

Physics Talk

• Conserving energy
• KE GPE and EPE are the different types of energy
• EPE is the energy stored in a spring due to its compression such as bungee cords or trampolines
• The total energy is always the same of an object even though each energy separately can vary
• Not only the engery but the joules always have to be the same too
• GPE is at the bottom on the compressed toy
• KE and GPE and when the toy is just released off the table are always the same as the KE and GPE while its still popping along with the GPE when it reaches it's highest point
• the more mass on the toy the less the hight will be
• a lighter toy will go farther and the heavier toy will not travel as far even though their EPE will always be the same
• GPE = MGH
• When a roller coaster is at it's highest point it has it's largest GPE
• electrical energy- the energy used to pull a car up an incline
• thermal and sound energy are the only things that can effect a change in the GPE and KE
• KE becomes thermal energy when the cart stops
• springs are used as substitutes if the breaks fail
• SPE = 1/2(k)(x^2)
• K = spring constant
• X = the amount of stretch or compression by the spring

Checking up Questions

1.

• It will have both kinetic and gravitational potential energy when it bounces off the table

2.

• It would equal 2 joules of KE

3.

• At the highest point it will have 2 joules of GPE

4.

• It would be the spring constant and the distance it is compressed.

Physics to Go

5.

• It wouldn't work if it was higher because than it wouldn't have enough energy or GPE to successfully pass over the second hill

6.

• There won't be enough energy because there is friction that is not working in the rides favor.

7.

• (300)(10)(15)= 45,000 joules - the energy it takes to raise the car

8.

• KE = 1/2 mv^2
• KE = 1/2 (400) (15)^2
• 45,000 joules
• KE = GPE
• 45,000 joules
• 45,000 = (400)(h)(9.8)
• 11.48 m

9.

• The GPE would be higher because the height is going to be higher

10.

• If the heights are all the same then they will all have the same GPE because GPE = MGH

11.

• GPE = KE
• .0782 = .073
• GPE = (0.02)(9.8)(.4)
• GPE = .078 J
• SPE=KE
• SPE= 1/2 mv^2
• SPE= 1/2 (0.020)(2.7)^2
• SPE= 0.0729 J
• KE = GPE
• 1/2mv^2 = mgh
• 1/2 (.006)(2.7)^2 = (.006)(9.8)h
• .02187 = .006(9.8)h
• h = .37 m

12.

• GPE = SPE
• mgh = 1/2kx^2
• 300(9.8)18 = 1/2k(4^2)
• k = 6615 m/m
• GPE = SPE
• GPE = mgh
• 400(9.8)(18)
• 70,560 = 1/2 kx^2
• 70,560 = 1/2(6615)x^2 joules
• x = 4.62 m

13.

• KE = SPE
• KE = 1/2kx^2
• KE = 1/2 40(.3)^2
• KE = 1.8 joules

What do you think Now?

• By using cables motors and different types of electronic energy roller coasters now a days can reach their maximum thrill. It maybe be a little bit extra money to provide for the extra cost of the added GPE but the amount of people who will pay to go on the rides will cover for it. The extra electricity being used may cost more for the amusement park but it will create a much better and more exciting attraction for everyone to admire.

Section 4

What do you see?

• There are kids on a roller coaster on the moon that look really bored and then there are kids on Jupiter next to them that look like they're having a lot of fun.

What do you think?

• All gravity points towards the earth and that is why people on the bottom of the earth are even held onto the surface. Technically there is no part of earth that is upside down it is just the part that is opposite to where you are. Where all the gravity will still remain the same.

Physics Talk

• Newton's Law of Universal Gravitation
• gravitational field- the gravitational influence in the space around an object
• First object - earth
• Second object - moon
• they share an inversed squared relationship which is - he relationship between the magnitude of a gravitational force and the distance from the mass. this also describes how electrostatic forces depend on the distance from an electrical charge
• the farther from the surface of the earth the gravity becomes less
• force of gravity between 2 objects decreases by the square of the distance between them which is an inversed squared relationship
• x3 = 1/9
• x4 = 1/16
• x5 = 1/25
• Newtons law of universal gravitation- all bodies with mass attract all other bodies with mass
• the force is proportional to the product of the two masses and gets stronger as either mass gets larger
• the force decreases as the square of the distances between the two bogies increases
• the force of attraction between two bodies due to their masses
• Newton's law of universal gravitation: fg = (G(m1)(m2))/r^2
• Fg = force between the bodies=
• R = the distance between their centers
• m1 and m2 = masses of the bodies
• G = 6.67 x 10^-11
• Moon orbits earth
• Planets orbit the sun

Checking Up
1.

• It will always be facing towards the ground because that is where the gravity is pulling

2.

• The closer to the earths surface the stronger the gravitational force

3.

• It would be 1/9 because 3^2 is 9

4.

• Its the force that holds the moon, earth, and planets in orbit around the sun

5.

• It's ver close to an elliptical orbit

Physics to Go

1.

• 125 Newtons because of the 1/4 inverse squared relationship

2.

• The force would be 1/4 of original
• The force would be 1/9 of the original
• The force would be 1/16 of the original

3.

• Gravity keeps us planted on the earths surface and that is why we have gained so much trust in it. It's not like you see people floating around in the air and that is because gravity keeps us attached to the surface there will always be gravity unless you can go on the moon or out onto other planets in the solar system.

4.

• It's higher gravity than at the bottom of the coaster so the acceleration must be greater.

5.

• The water on the side of earth that is towards the moon is closer to the moon than the middle of earth
• The water moves independently which causes high tides on the side of earth where the moon is. It is only this way because water does not have as dense of a mass as everything else on earth does there for the gravitational force is less.
• The land on most of the earth causes the uneven distribution of water on the surface.

6.

• The gravity holds the fish in the water and without it then the fish would be in the air and would suffocate
• A fish has a smaller mass than the earth therefore the gradational force is present

7.

• 1/4
• 1/9
• 1/16
• x4

8.

• 2x
• 3x
• 4x
• 1/2x

9.

• 4x
• 9x
• 16x
• 1/16x

10.

• 2x
• 9x
• 6

Physics Plus

1.

• a = v^2/r

2.

• v = d/t
• (2)(pie)(3.84x10^8)/2440800
• v = 998.5 m/s

3.

• a = v^2/r
• a = 998.505^2/3.84x10^8
• a = 0.025 m/s

What do you think now?

• The direction on gravity is the force that there is pushing on an object. Everything is pulled toward the heaviest thing which in this case would be the earth. And nothing we know of weights as much or more than the earth and that is why nothing can float in the air. Gravity still applies to these people towards the bottom of the globe because they are still attracted to the center of the earth no matter what position that they are in.

Section 5

What Do You See?

• They are in a deli and the meat is on the scale and is being weighed. When the meat is put on the scale then the scale moves down. In this picture they are using a regular scale to weigh that meat but in the lab that we are going to do we have to use a spring scale. It shows that there are many different ways to weigh things and they don't all have to be weighed using an electronic scale.

What Do You Think?

• Weighing an elephant on a scale that you used to weigh a canary wouldn't work because the canary would weigh so little compared to the elephant that you won't even be able to tell what the bird weighs and it will probably show up at 0. If you tried to weigh an elephant on the canary's scale that wouldn't work either because the elephant wouldn't fit on the scale or the scale would not be able to weigh the elephant.
• W= m(g) is the equation we use to measure our weight on an electronic scale.

Physics Talk

• Hooke's Law:
  • restoring a force exerted by a spring is directly proportional to the distance of stretch or compression of the spring
    force exerted by the spring
  • -spring constant(spring stretch)= Fs
  • Fs=-kx
  • The negative k shows that the stretch and the compression of the spring are opposites
  • create by Robert Hooke because he created the property of a spring
  • stretching and condensing a spring uses a force
  • the force required and the stretch of the spring are directly proportional
  • If there is a big force then the stretch of the spring will be bigger
  • If there is a small force then the stretch of the spring will be smaller
  • If the spring is at rest then there is no force
  • A largely expanded spring will have a large k
  • A loose spring will have a small k
  • force = ma
  • weight is a measurement of mass
  • the weight is the mass times gravity with is 9.8
  • To get an accurate measure on a scale when you step on springs inside compress
  • depending on how much or little the spring compresses then you can determine your weight
  • this does not work for everything though because there is a limit and a minimum on each one of these scales and they are also are in all different units

Checking Up

1.

• If the force of the spring is increased by 5 then the stretch of the spring is also increased by 5.

2.

• The spring constant represents how hard or easy it is to compress a spring or stretch it.

3.

• The weight of an object in newtons is equal to it's mass in kgs and mass is a part of weight.

4.

• The more weight then the more compression of the spring.

Physics to Go

1.

• W=mg
• W=100(9.8)
• W=980 N
• W=mg
• W=10(9.8)
• W=98 N
• W=mg
• W=60(9.8)
• W=588 N

2.

• .25/130=1/x
• x=520 N
• .25/1000=1/x
• x=4000 N
• .25/50=1/x
• x=200 N

3.

• 
• 0.1491 N/m=14.91 N/m
• slope = the spring constant
• It would have more stretch because it's looser and has a smaller slope.

4.

• F=k(x)
• 12 N=k(.03)
• k=400 N/m

5.

• The force and the stretch are directly proportional as the the more force used to stretch the spring the larger force that is going to be required to put it back together. Same thing is the force is smaller to pull it apart then the force will be smaller to put it back together.

6.

• The higher spring force constant the higher the slop which means that it will be harder to stretch so that means 15 would be the hardest to stretch because it has the largest spring force constant.

7.

• F=k(x)
• 3 N=k(.02)
• k=150 N/m

8.

• Hooke's law defines the measure of weight on a spring scale. The force and the stretch of this string equal each other, the farther the spring is pulled the stronger the force required the smaller the spring is pulled the smaller the force is.

What do you think now?

• There is no way they you could use the same scale to weight two completely different size animals because the spring can only compress to a certain amount so it can only get so small or so big. The bird is only a fraction of size of the elephant so you would not even be able to tell the weight of a bird on the scale used for an elephant and vice versa.
• Bathroom scales are used also by just seeing the compression of a spring as weight is added then the springs compress and depending on how much the springs compress then weight is determined by using F=-k(x).

Section 6

What do you see?

• There is a little man riding up an elevator and the scale reads 200 pounds then there is a fat man in an elevator riding down who is standing on the scale and has a weight of 0.

What do you think?

• Your weight never really changes. You will always weight the same amount but sometimes depending on the activity you're doing weight might seem to be heavier or lighter. If you are moving, then the forces that are acting on you change. The larger the force the more weight you are going to weight and the less force the less weight, but your real weight will never be altered unless you gain or lose weight.

Checking Up Questions

1.

• When the object is moving at constant speed the sum of its forces are always going to be 0.

2.

• When accelerating up on a bathroom scale on a roller coaster the scale will weight more because the net force pushing down on you will be stronger.

3.

• You never really weight more, but you feel like you do because the forces pushing down on are you are stronger.

4.

• If the elevator cable broke you would weigh 0 on the scale because you, along with the scale are free falling, you would feel as if you were floating.

5.

• The raindrops are slowed down by air resistance, which we normally ignore.

Physics Talk

• An object at rest stays at rest until another force acts upon it, an object in motion stays in motion until another force acts upon it (Newton's First Law)
• If an object is at rest it's acceleration and net force will always equal zero (Newton's Second Law)
• If an object is moving at constant speed its acceleration and net force will also equal zero (Newton's Second Law)
• Your weight is your actual weight if you are moving at constant speed or are at rest
• If you are accelerating up then your weight will be more than what it actually is because of the force pushing down on you
• If you are accelerating down your weight will be less because there is a force helping you move down
• If the roller coaster or elevator is accelerating you are accelerating or decelerating also
• you move with the roller coaster or elevator like you are a part of it
• When the forces combine to make a stronger force then it can either be smaller or larger
• If the forces are going opposite ways then your weight will remain the same because they cancel out each other
• You will feel like you weight less while accelerating down and you will feel like you weight more when you're accelerating up but you actually weight the same and it's just an illusion

Physics To Go

1.

• vf=vi(0) + at
• vf=at
• 9.8(2)=19.6 m/s
• 9.8(5)=49 m/s
• 9.8(10)=98 m/s

2.

• vf=at
• 1.6(2)=3.2 m/s
• 1.6(5)=8 m/s
• 1.6(10)=16 m/s

5.

• They were either experiencing increased downward acceleration or decreased upward acceleration.
• since ma= a negative number and v is ^ and a is v
• the only two answers could be increased downward acceleration or decreased upward acceleration

6.

• Her weight will only increase because of the increased upward acceleration because the force is stronger on the girl when they are moving up and she will as a result feel heavier.

7.

• the weight shown on the scale will get smaller
• fnet=m(a)
• W-fscale=m(a)
• 50(9.8)-fscale=50(1.5)
• fscale=415 N

8.

• net force = 0
• fscale-w=m(a)
• fscale-50(9.8)=50(2)
• fscale=590 N
• 0 because it's traveling at a constant speed

9.

• When you're not moving or moving at constant speed the weight on the scale will always be 0 because the forces are equal and opposite so they cancel each other out.
• It would be 0 because you are free falling.
• There is a bigger force pushing down on the person if you're accelerating upward so there for if the force is larger then the weight shown on the scale will be larger also, even thought that number is not the persons actual weight, they will still feel heavier.

10.

• They would like the areas where you would feel heavier and lighter in the roller coaster such as during increases and decreases in acceleration and during the loops and the turns.

What do you think now?

• Your weight never really changes but depending on the forces acting on you they could make you appear to weight more or weight less. The larger the force, the greater the scale will go up, the less the force, the more the scale will go down. But if you're ever just moving at constant speed or at rest the reading on a scale will be accurate.

Motion of the Elevator	Acceleration (up, down, zero)		Relative Scale Reading (greater, less or equal to weight)
At rest, bottom floor	zero		equal
Starting at Rest, Increasing Up	up		greater
Continuing to move, Constant Up	zero		equal
Slowing down to top floor, Decreasing Up	down		less
At rest, top floor	zero		equal
Starting at rest, Increasing Down	down		less
Continuing to move, Constant Down	down		less
Coming to a stop on the ground floor	up		greater

Section 7

What do you see?

• In the picture there's a cart that's moving up and down hills and through loops and when the cart moves through a curve then all of the people shift over to one side of the cart.

What do you think?

• You don't fall out because the momentum that the cart has and the sides of the cart keep you glued to the seat and then the velocity that the cart has keeps it stuck to the track. The track keeps the cart in place so that it does not move or slide like the people do when they are going through a curve.

Physics Talk

• Centripetal force
  • any force thats directed towards the center of a circle
  • this causes an object to follow the path around the circle at a constant speed
  • the faster the speed the larger the centripetal force
  • the slower the speed the smaller the centripetal force
  • when the centripetal force gets bigger the mass also gets bigger while the radius gets smaller
  • Fc = mv^2 / r
• Centripetal acceleration
  • acceleration directed towards the center of a circle
  • this remains constant while traveling in a circle
  • the force of the person in the roller coaster against the cart causes the acceleration
  • the faster the acceleration the greater the thrill
• Vectors
  • at the bottom of a circle
    • normal points up
    • gravitational points towards the center
  • at the top of a circle
    • gravitational points down
    • normal force points down also
    • net force will be facing down
• The acceleration and weight of the car can determine how much force will be required to get the cart to move
• weight is the same throughout no matter where you are in the coaster but at the top you will feel lighter and at the bottom you will feel heavier but you actually weigh exactly the same
• Weight
  • at the top
    • feel lighter
    • acceleration is down
  • at the bottom
    • feel heavier
    • acceleration is up
  • on a level plane
    • the sum of all of the forces are 0 because you're are either moving at constant speed or are at rest

Checking Up Questions

1.

• You need centripetal force for an object to travel in a circle

2.

• Centripetal acceleration because you are moving at constant speed in a circle

3.

• You would add the gravitational and normal forces to find the centripetal force

4.

• The normal force gives you your weight

5.

• The faster the speed the larger the centripetal force the larger the centripetal force the larger the weight and the smaller the radius

Physics to Go

1.

• It would move in the path of a circle
• The car would then move in a line that is tangent to the circle that it was previously moving in

2.

• Instead of the string it would be friction instead

6.

• It would still be 20 m/s
• It changed because the direction also changed
• It was changed to 28 m/s at 45 deg. north west
• find the change in v
• 20^2+20^2=c^2
• c=28 m/s
• tan of the angle=20/20
• the angle=45

7.

• Ac=v^2/r
• Ac=20^2/200
• Ac=2 m/s^2

10.

• A high thrill roller coaster

	Required Fc	Force of gravity (w)	Normal force
bottom of loop	4000 N	500 N	3500 N
bottom of loop	6000 N	500 N	6500 N

• Small thrill roller coaster

	Required Fc	Force of gravity (w)	Normal force
top of loop	800 N	500 N	300 N
bottom of loop	2800 N	500 N	3300 N

13.

• 1 - heavier
• 2 - can't tell
• 3 - heavier
• 4 - heavier
• 5- no change

14.

• 1 - up
• 2 - down
• 3 - up
• 4 - up
• 5 - zero
• 6 - to center
• 7 - to center

Physics Plus

1.

• The mass will increase which then makes the net force increase
• Because of the inverse squared relationship will be quadrupled

2.

• You would multiply it by 4

3.

• They are indirectly proportional so it would get smaller

4.

• The bigger the radius the smaller the force to keep it moving

5.

• There would be no force acting upon it so it would just continue in a straight line ( Netwon's first law )

What do you think now?

• You can't fall out of a roller coaster because inertia is keeping you pushed against your seat. The normal centripetal and gravitational forces will keep you in the cart at all times while you're moving. If you were stopped upside down then you would fall out but because you are moving all the time you can't possibly fall out.

Section 8

What do you see?

• There are people pulling a cart up a hill that's very tall and you can see that they're sweating but after the cart reaches the climax of the hill then it speeds down without anyone having to even touch it

What do you think?

• Because the slope of the hill is greater than i think that it will take more force and energy to pull the part up the hill. You don't need as much force and energy to go up a smaller hill because the slope is smaller.

Physics Talk

• Work
  • is the product of displacement and force
  • it's a transfer of energy
• w=f(d)
  • work = force x displacement
• the work is always the same no matter what the slope is
• as the incline gets bigger so does the force
• if the incline gets bigger than the slope will get smaller
• you need work for the cart to move up an incline
• the more work you use the more energy you're using
• vertical displacement
  • how high the cart must be
• a motor supplies energy to the cart to complete the work
• work is done using a spring
• work is also done by using friction and air resistance
• you need breaks to stop a roller coaster safely
• kinetic energy turns into thermal energy which creates the breaks
• power
  • the work divided by the time
  • the speed that work is done
  • p = w / t
• units of power
  • watts

Checking Up Questions
1.

• The energy then converts to gravitational potential energy while it is going up the incline

2.

• When you find the work that is being done then you can find the gravitational potential energy from the work that was done using a spring

3.

• Since the force is small that means that the slope is small so that there is less work and then it is easier to get up the hill. If the slope was larger then it would require more work and it would be harder to get up the hill. You need to lift to a certain height and if the distance is larger and the slope is smaller the work is always smaller

4.

• Kinetic energy is then converted to thermal energy instead

5.

• Power is measured in watts

Physics to Go
1.

• the gravitational potential energy is always higher at the top of the hill than at the bottom
• the work turns into gravity so that you don't need to do any work because the cart is accelerating by itself
• when the spring compresses then it turns into work
• spe=1/2(k)(x)^2
• It would be the gravitational potential energy
• Only when the cart first starts to touch the spring

2.

• W=F(d)
• 0 = W
• W=F(d)
• W=60(.5)
• W=30 N
• W=F(d)
• W=75(40)
• W=3,000 N
• W=F(d)
• W=500(.7)
• W=350 N

3.

• You would just say conserving the energy according to a certain problem or in this case roller coaster instead of just saying energy in general.

4.

• The mass would grow along with the force so the distance would become smaller if we wanted the work to stay the same then the every would also increase too

5.

• W=F(d)
• W=10,000(20)
• W=200,000 N
• P=work/t
• P= 200,000/150
• P= 1/3 J

6.

• When you're going up gravitational potential energy gets bigger because the work is getting bigger but then when you get to the top of the first hill you no longer need any work because then the cart takes all of the work and energy used to move up the hill and releases it to go down.
• up first hill- work to gravitational potential energy
• down first hill- gravitational potential energy to kinetic energy
• top of loop- kinetic energy only
• up second hill- gravitational potential energy and kinetic energy
• horizontal loop- kinetic energy only
• braking at the end- work only

What do you think now?

• The bigger the slope the harder is it to pull a cart up and the more energy and work that is going to be needed to get up the hill. The weight is always equal to the gravitational potential energy which would mean the force times the distance is equal to the mass times gravity times the height. The smaller the incline that something is then the less work that is needed to go up it. As a result this obviously makes it easier but the distance in the end will be longer because you decreased the slope.

Section 9

What do you See?

• There is a girl sitting at desk thinking about a roller coaster with a bunch on calculations regarding energy. The boy that is sitting next to her looks like he is trying to think about roller coasters and their force but on the paper it is blank.

What do you Think?

• The part of the roller coaster that would be the most exciting part would be when the roller coaster is moving from side to side because there would be a change in the velocity because the direction is changing.

Physics Talk

• vectors are measured with numbers and direction
• scalar is a vector that is only numbers
• total energy is always the same through out a roller coaster
• the only thing that varies is the gpe and the ke
• the gpe and the ke always add up to be the same thing (total energy)
• the gpe is based on the height mass and gravity
• if two carts on different roller coasters have the same mass they will have the same speed
• they will not end up at the end of the roller coaster at the same time though
• the steeper a slope the larger the gpe

Checking up Questions
1.

• You would have to use pythagorean theorem to solve that problem

2.

• The energy would be a scalar quantity and the force would be the vector

3.

• Gravitational potential energy along with kinetic energy will always be equal because the gravity and the mass always remain constant.

4.

• It wouldn't effect it at all

5.

• You would need work or another force

Physics Plus

1.

• a^2+b^2=c^2
• 5 ^2+5^2=c^2
• 50=c^2
• c=50 m/s SW
• tan(x)=5/5
• x=45 degrees

2.

• The gravitational potential energy would be the same because the height is also the same along with the velocity and the kinetic energy

3.

• distance, scalar
• displacement, vector
• speed, scalar
• velocity, vector
• acceleration, vector
• force, vector
• kinetic energy, scalar
• potential energy, scalar
• work, vector

4.

• scalar
• vector
• scalar
• vector

5.

• Energy-
  • KE and W to get up the hill
  • GPE at the top of the hill
  • KE down the hill
• Force-
  • The more weight the larger the force
  • The normal force gets smaller when the weight gets larger

6.

• It would be simpler for the second roller coaster because there are no curves or hills and the normal force is always measured perpendicular to the track

7.

• The energy is the same at every point because all the heights are the same
• The KE would still be the same because the height is the same
• The gravitational potential energy must always equal the kinetic energy

What do you Think Now?

• When there is a change in direction it will be the most exciting part of the ride because this is the only time when the speed will change because the direction is also changing. I know that if i had to pick a ride i would pick one with many turns and loops and drops because they seem so exciting.

Section 10

What do you See?

• It looks as if there are a ton of cars racing down these raps that were set up. All of the ramps are different shapes and sizes and it looks as if the people are falling out of their cars. The cars are also falling off of the tracks. This looks extremely dangerous and unsafe.

What do you Think?

• If the roller coasters that are so dangerous that people could die that doesn't make them fun. We have to be so careful with the way that these coasters are build so that they are safe yet fun. Anyway an amusement park usually would not allow a roller coaster that people have died on to remain working.

Physics Talk

• if the acceleration of a cart is under 4 g's at all point on a roller coaster it is considered safe
• a(c)=v^2/r
• normal force and weight are always acting on the roller coaster
• if the value is over 4 g's you can
  • increase the radius
  • make the velocity smaller
  • reduce the height
  • change the position
• free falling object has acceleration of 1 g
• centripetal acceleration always points to the center of the circle
• a car at rest has a net force of 0
• a car moving at constant velocity has a net force of 0
• as the number of g's increase, the heavier your body will feel

Checking up Questions

1.

• 4 gs is the maximum acceleration that it can be for the roller coaster to still be safe

2.

• If you decrease the height then the energy will also decrease and as a result the velocity will be smaller

3.

• At the bottom of the loop

4.

• At the top of the loop

Physics To Go

1.

• I would check the accelerations at each of the points to make sure that it is under 4 gs. This will ensure that the people wont be killed or knocked unconscious. I would also check to make sure that the cart is going fast enough around the loop. If it isn't, the cart won't be able to make it over the loop.

2.

• 20 m
• a=v^2/r
• a=20^2/12
• a=400/12
• a=33.33 m/s^2
• No it can't be safe it's over 4
• 4=39.2 m/s
• 39.2=v^2/12
• 470.4=v^2
• v=21.69 m/s
• 39.2=v^2/7
• 274.4=v^2
• v=16.57 m/s

3.

• a=v^2/r
• a=25^2/10
• a=62.5 m/s^2
• yes it would be under 4 so it would be considered a safe amount of acceleration

4.

• gpe=mgh
• mgh=mv^2
• 9.8(50)=v^2
• 490=v^2
• v=31 m/s
• a=v^2/r
• a=22.14^2/10
• a=96 m/s^2
• v= the square root of (a)(r)
• v= the square root of (49.02)(10)
• v=22.14 m/s
• 58 m/s
• The acceleration is under 4 so it's safe

5.

• mgh=mv^2
• 9.8(16)=v^2
• v=8.9 m/s
• gpe=ke
• mgh=1/2mv^2
• 9.8h=1/2(12.52)^2
• h=20 m

6.

• a=v^2/r
• a=12^2/18
• a=8 m/s^2
• f=mv^2/r
• f=900(12)^2/18
• f=7,200 N
• The weight and the F(c)

7.

• a=v^2/r
• a=20^2/15
• a=26.67 m/s^2
• f=mv^2/r
• f=900(20)^2/15
• f=24,000 N
• The ride can exert 1,000 more than the cart can

8.

• It won't change
• Changing the mass wont effect it
• It'd have to be more sturdy

What do you Think Now?

• People only go on rides that are safe like the ones from six flags or well known amusement parks. If people thought that these rides put you in danger then no one would go on them. Everyone knows that just a ride on a roller coaster isn't worth your life and that you could get the thrill from something else. One thing that these roller coaster creators have to be very careful of are the fact that the acceleration could not be over 4 gs because if it is then the people would fall out of the ride or the roller coaster would not be able to stay on the track. If the acceleration is too small though then you won't be able to make it around the whole roller coaster or any of the loops and then it can become dangerous also.